Harmonic analyzer



L. W. CHUBB.

HARMONIC ANALYZER APPLICATION FILED DEC.31, 1913. RENEWED JUNE 28.1916.

Patented Dec. 2, 1919.

F/ J0 J m I Harmonic Analyzers.

4 UNITED STATES rArn LEWIS W. CHUBB,.OF EDGEWOOD PARK, PENNSYLVANIA, ASSIGNOR T0 WESTINGHOUSE V I r ELECTRIC AND MANUFACTURING COMPANY, A CORPORATION OF PENNSYLVANIA.

HARMONIC ANALYZER.

I Specification of Letters Patent.

Patented Dan, 1919.

Application filed December31, isiase naino.809,724; I Renewed June 28; 19 16. Serial Ito/106,519;

To all whom it may concern: 7 Be it'known that I, LEWIS W.-CHUBB, a itizenof the United States, and a resident of Edgewood Park, in the county'of Alle-, gheny and State of Pennsylvania, have invented a new and useful Improvement in I of which the following is a specification. V

My invention relates to harmonic lyzers and particularly to types of the same for analyzing composite curves having circular or polar coordinates. r

The object of my invention is to provide a harmonic analyzer for mechanically determining the amplitude of the sine and cosine components of any harmonic component of a periodic function.-

Heretofore, several types of harmonic analyzers have been provided but thesewere all adapted to analyze curves plotted in rectangular coordinates and they depended in most cases upon friction or the extension of springs for the force by which they were operated. -My invention has many advantages by reason of the fact that it is adapted to analyze curves plotted in polar or circular coordinates, and it operates positively from gear wheels and other mechanical devices so that there is a great saving of time, and greater accuracy assured; Serial No. 809,795, describes a methodof producing oscillographic waves having polar or circular coordinates which may be usedin my present invention,as hereinafter described.

Figure 1 of the accompanying drawings is a view, partially in plan and partially in section, of a harmonic analyzer embody-l ing my invention, Fig. 2 is a front elevational view of the harmonic analyzer shown in Fig. 1, Fig. 3 is a sectional view taken along the line IIIIII of Fig. 1, Figs. 4 and 5 are diagrammatic views of a harmonic analyzer and the curves described when the same is operated, and Fig.

o is a detail view of parts of my invention.

Referring to the drawings, I provide a base member 1, two guide rails 2and 3', and two end plates 4 and 5 forming a rectangular receptacle, substantiallylas shown. A

keyway 7' cut therein,

My copencling application,

rotatableshaft 6, having is supported between the end plates 4:H11d' 5 and is provided with a worm screw 8 having a-"pin 9 that'slides in the keyway 7, to alow'of a rectilinear motion-,as hereinafter explained; Oneend of the shaft 6 isscrew-threaded toreceive a nut 11 for holding a gear wheel 10in place. A second rotatable shaft 12 1s also supported between the end plates 4 and 5 and has securely keyed theretola" worm screw'l3 that engages aworm wheel 14 ha ving a shaft or arbor l4 whlch is mounted he base 1. The front end of the shaft 12' is screw-threaded to receive 'a'nut 15 for holding a gear wheel 16 in place. A bell crank lever 18 is loosely mounted upon the front bearing 17 of theshaft 12, and one arm 19 of the same has a slot 20 therein in which is adjustably mounted-an arbor 21'. Two gear wheels 22 and 23 'andan operatinghandlc '24 are mounted on the arbor 21 and are held in place by a nut'25. The other arm 26 of the bell crank lever18 h'asa curved slot 27 therein into which projects a stationary screw 28 that is supported by the front plate 5 and, when tightened, maintains the lever 18 in any desired posi-- tion. i

The 'worm wheel 14: has a diametral graduated slottherei'n for receiving a movable crank pin 29 whlch'is retained 1n any upon the rails 2 and 3 and has rotatably, mounted thereon an arbor 32 carrymg a yr OFFICE.

a relatively long turn table 33 and a worm wheel 34i, the lat ter of which is engaged and driven by the sl'idable worm screw 8. On each side of the carriage 31 is a bifurcated'standard 35 for guiding a rod 36. The rod 36 has a pin 37 projecting therefrom that has a' groove 38 inits lower end for engaging a templet 3S) the periphery of which conforms to the cir- -cular or polar coordinate representation of the curve to be analyzed. The templet is attached to the center of the turn table by a nut 41 which fits the screw threaded end of the arbor 32, and two springs 40 hold the pin 37 in engagement with the periphcry of the templet as the turn table rotates.

At the end of the rod '36 is a hole as to receive a pin that is located in one end of a planimeter 43 which has the usual vernler wheels 44: that roll upon a table 45 and integrate the area or" the curve representing the harmonic being investigated.

The gear wheels 10, 16, 22 and 23 have such numbers of teeth that the carriage 31,

starting at the front of the instrument, will make as many complete oscillations as is the order of the harmonic being investigated during the time that the turn table has r0- tated 360, 1f the curverepresented thereon by the templet is for one complete cycle. A complete set of gear wheels is provided for A templet 39 of the circular or polar co ordinate representation of the composite curve to be analyzed is made and is placed upon theturn table, substantially as hereinbefore described, with the carriage in its extreme front position and with the gears arranged for the correct rotation for the particular harmonic to be investigated. The operation is as follows: 7

The handle 2e 's turned to the right and the carriage is moved toward the rear and returned to the front as many times as is the order of the harmonic, while the turn table rotates one time. As an example, if the amplitude of one quadrature component of the third harmonic is being sought, the carriage retires and advances three times while the turn table rotates once. The groove 38 in the pin 37 engages the templet 39 and the rod 36 is given motions in two directions to draw a figure, if a pencil is placed in its end, substantially as shown in Fig. 4. Then the area of this figure divided by the product of the order of the harmonic times 3.1 116, multiplied by the radius of the crank pin 29, will be the amplitude of one component of the third harmonic belng sought. Since the drawing of the figure and then its integration is complicated, and mistakes are liable to be made, the planimeter 4:3 is utilized and is inserted in the hole e2, as

hereinbefore described, and the actual area of the curve which would be drawn is read from the Vernier wheels 44 and the follow ing formulae, as hereinbefore stated, is applied.

A as 'mrR where A zamplitude of the sine or A component of the nth harmonic,

the nthharmonic, the screw 28 is loosened and the bell crank lever 18 is rotated about its axis until the gear wheels 22 and 10 are 7 disengaged, then the screw 28 is again tightened and the handle turned, driving the shaft 12 until the cariage moves from the front to the center of the device without rotating the turn. table. Then the screw 28 is again loosenedand the gears 10 and 22 7 again engaged and the handle is rotated as described with reference to the sine component. The carriage moves backwardly, returns to the center, then to the front and again to the center n times for the nth har monic while the turntable rotates one time. 1 L I v i lhe amphtuce or the cosine component of the nth harmonic is then h B as before nvrR where K B zamplitude of the cosine or- B component of the nth harmonic,

S :area of the figure described by the point of the rod 36 or planimeter reading,

7: :3.1L16,and L R :distance betweensthe centerof the worm gear 14 and the center of the pin 29 or one-half the travel of the carriage.

Thus, any curve may be analyzed to find the two quadrature components of the various harmonic waves which combine to form the composite wave being analyzed. The amplitude of the nth harmonic without respect to phase difference is equal to the square root of the sum of the squares of the A and B or sine and cosine components of the nth harmonic, or

as is well known by'those versed in the art, where (3,:amplitude of the nth harmonic wave, I A zamplitude or co-efiicient of the sine component of the nth harmonic andr B zamplitude or co-efiicient of the cosine component of the nth har monic. Referring-now particularly to Fig. 4e,the proof for the determination of the sine component follows: Y

- liereinbefore stated.

: When the carriagestarts at the bottom, it moves upward making n oscillations for the nth harmonic while the turn table rotates one time, substantially ashereinbe fore stated, the following is true for values of y and a: or the ordinates and abscissas respectively Me os) R cos n0 (2) and FA, sin 0+A, sin 36. A sin n6+B, Co

6+B cos 3Q). +B, cos n9 from Fouriers series.

then from equation (2) g #723 sin n6 (4) The area of the figure traversed by the V 21r I S =f A nR(sin n6)i'6 (6) from which by solving and simplifying v S =A nR1r or V i mrR (7) V where A S m and R are the same as With special reference to Fig. 5, sine or B component is obtained as; follows: The carriage is started' in the center and moves upward, considering (i zero at the point where the contact point touches the templet. The equations in this case for m and g are as follows:

y=R sin n6 (1a) x= f(6) =A sin 0+A sin 30+ A $111 at '+B cos 0+1? cos 36+: +13, cos

n6 (2a) I and as before the area of the figure is 2, t s =f xdy (3a) and from equation (1a) dy=nli cos he d6, then substitutingin equation (a). and simplifying terms thefolloWirigis true.

113,53 cos nmda 4a and integrating w 7 whereiB' S5, n, R and .m: are the same as hereinb'efore stated. Thus, from thefore 0-- proof of the hereining, may be seen the. before stated formulas. I

While I have described my invention in its preferred form 1,1 desire'it to be under-f stood that structural modifications may be made. which do not depart from the spirit I and scope of the same as defined in the ape pended claims, v e

1 I claim as my invention: 1. A" harmonic analyzer; comprising an oscillatory member, a rotatablemember mounted on the said oscillatory member and adapted to support la-templet and gear. 7 Wheels for oscillating the said oscillatory member a predetermined number of times while the rotatable member rotates onetime.

-2. A harmonic analyzer comprising an oscillatory member, a a rotatable 'member mounted on the said oscillatory member and adapted to support a templet, gear wheels for oscillating-the said oscillatory member a predetermined niunber of times while the rotatable member rotates" one time and a tracing device actuated by the rotation of- J the templet andthe oscillation of the oscillatory member foritracingxa figure the area of which is proportional to the amplitude of one component of one harmonic: of the curve rep-resented by the said templet.

3 A-harinonic analyzer comprising an oscill-atory member, a rotatable member mounted onithesaid oscillatory member and adapted to-carrya templetanda plurality of gear wheels for causing the said oscillatory member to oscillate apredetermined number oftimes while the rotatable member rotates one time. p r s 4:. ,A hZIIIXlOlllC' analyzer comprising an oscillatory member, a rotatable member mounted thereon, a templet of the composite curve to be analyzed mountedupon the said rotatable member, means for operating-the said rotatable and oscillatory members and a second oscillatory memberzmovably attached to the first oscillatory member and m operative engagementwith th'esaid tems 5." A harmonic analyzer comprising an oscillatory member, a rotatablemembermount' ed thereon, a polar coordinate templet of the curve to be analyzed mounted upon the said rotatable 'member and meansad-i V justable to control the number of oscillations of the oscillatory member during one rotation of the said rotatable member so that the former shall be in direct proportion to the order of the harmonic being investigated.

6. A harmonic analyzer comprising a polar coordinate templet of the composite curve to be analyzed, positive actuating means for oscillating the templet a predetermined number of times while it rotates one time and means actuated by the templet for tracing a figure.

7. A harmonic analyzer comprising, an oscillatory member, a rotatable member mounted on the said oscillatory member, a polar coordinate templet of-the composite curve to be analyzed mounted upon the said rotatable member, means for operating the said rotatable and oscillatory membersat predetermined relative speeds, a second oscillatory member movably attached to the first said oscillatory memberandin opera tive engagement with thesaid templet and meansoperatiyely connected to the said second osoillatorymember for measuring the area of the figure traced by the same.

8. A harmonic analyzer comprising an oscillatory m ember,- a rotatable member mounted thereon, a polar coordinate templet of the composite curve 'tobe analyzed mounted upon the said rotatable member, means for operating the said rotatable and oscillatory members at predetermined relative speeds, a second oscillatory member movably attached to the first oscillatory member, means for retaining the same in operative engagement with the saidtemplet, and meansoperated by the said second oscillatory member for measuring the area of the figure traced by the same. Y i l 9. A harmonic analyzer comprising an oscillatory member, a rotatable member mounted on the said oscillatory member, a templet of the composite curve to be analyzed mounted upon the said rotatable member,

7 means for operating the said rotatable and,

oscillatory members at predetermined relative speeds, a second oscillatory member movably attached to the first oscillatory member, means for retaining the same in operative engagement with the said templet and a planimeter operated by the said second oscillatory member.

10. A harmonic analyzer comprising an oscillatory carriage, a rotatable table mounted upon the saidcarriage, gear wheels for oscillating the said carriage a predetermined number of times while the said table 130-. tates one time and a rod movably attached to the said carriage and adapted to oscillate when the said carriage oscillates.

11. A harmonic analyzer comprising an oscillatory carriage, a rotatable table mounted upon the said carriage, gear wheels'for oscillating the said carriage apredetermined number ottimes while the said table rotates one time, a templetrepresenting the curve 1 times while it'rotates one time, and a tracing arm actuated by the said templet when it is oscillated and rotated to describe a figure that is a measure of-one component of one harmonic of the curve represented by the templet.

13. A harmonic analyzer comprising a templet of a curve to be analyzed, means for oscillating the templet a predetermined number of times while it rotates one time and means restrained in engagement with the templet for tracing a figure when the templet is oscillated and rotated.

14. A harmonic analyzer comprising a templet of a curve to'be analyzed, gear wheels for oscillating the templet a predetermined number of times while it rotates one time and means actuated by the templet for tracing a figure when the templet is oscillated and rotated.

15. A harmonic analyzer comprising a templet of a curve to be analyzed, gear wheels for oscillating the templet a predetermined number of times while it rotates one time and a planimeter actuated by the templet tointegrate the area of a figure In a harmonic analyzer, the combinathat is the measure of one component of the curve represented by the templet.

16. A harmonic analyzer. comprising an oscillating member, means for oscillating the oscillating member a predetermined number of times and for simultaneously rotating a templet of the composite curve to be analyzed one time, and a tracing arm adapted to be engaged by the templet when it is rotated for movement thereby to trace a figure. I 1 17. A harmonic analyzer comprising an oscillating member, means for oscillating the oscillating member a predetermined number of times and for simultaneously rotating a templet of the composite curve to be analyzed one time, and a tracing arm for so engaging thetemplet as to be actuated thereby when the templet is rotated and said arm cooperating with the said oscillating member to describe a figure thearea of which is a measure of one component of one harmonic ofthe curve represented by the templet. I

18. A harmonic analyzer comprising an oscillating member, a rotatable member adapted to carry a templet of the composite curve to be analyzed, means for causing the said oscillatory member to oscillate a predetermined number of times and for simultaneously rotating the rotatable member one time, and means actuated by the templet and the oscillating member for describing a figure.

19. A harmonic analyzer comprising an oscillating member, a rotatable member adapted to carry a templet, means for causing the said oscillatory member to oscillate a predetermined number of times while the rotatable member rotates one time, and means adapted to engage the templet and to cooperate with the rotatable and the oscil-' latory members for tracing a figure.

20. A harmonic analyzer comprising an oscillatory member, a rotatable member adapted to actuate a templet, means for causing the said oscillatory member to oscillate a predetermined number of times While the rotatable member is actuated one time, and means dependent upon the actuation of the templet and the oscillation of the oscillatory member for describing a figure.

21. A harmonic analyzer comprising an oscillatory member, a rotatable member adapted to actuate a templet, means for causing the said oscillatory member to oscillate a predetermined number of times while the rotatable member is actuated one time, means dependent upon the actuation of the templet and the oscillation of the oscillatory member for describing a figure, and means formeasuring the area of the figure.

22. A harmonic analyzer comprising an oscillatory member, a rotatable member member is actuated one time, and means de-' pendent upon the actuation of the templet and the oscillation of the oscillatory memher for integrating a value that is a measure of one component of one harmonic of the curve represented by the templet. V

23. A harmonic analyzer comprising means adapted to move with a simple harmonic motion, means actuated by a templet of'the curve to be analyzed and adapted to move with a rectilinear motion at right angles to the line of motion of the first mentioned means, and means actuated by the two said means for describing a figure.

24. A harmonic analyzer comprising means adapted to move with a simple harmonic motion, means actuated by a templet of thejco curve to be analyzed and adapted to move with a rectilinear motion at right angles to the line of motion of the first mentioned means, and means dependent upon the motion of the two said means for integrating a value that is a measure of one component of one harmonic of the curve represented by the templet.

In testimony whereof I have hereunto subscribed my name this 29th day of Dec., 1913. V

LEWIS W. oHUBB.

W'itnesses D. l/V. A. OETTING, V B. B. HINES. 

